I can duplicate your results on Windows 7. It looks like this is one of the many areas where software no longer fully supports Windows 7. This is inevitable and we users need to accept this reality and to work around it as best we can.
Meanwhile, the right-click Play option still works with the system default player in Windows 7. And you can create Mp3tag Tools to load other players, as discussed here. No drag and drop will be needed. And you will be able to upgrade to the current version of Mp3tag.